1. Fast Collision Detection for Deformable Models using Representative-Triangles Presented by Marcus Parker By Sean Curtis, Rasmus Tamstorf and Dinesh Manocha http://gamma.cs.unc.edu/RTRI

2. Collision Detection Triangulated models – Vertices, edges, faces Discrete collision detection (CD) – 6 elementary tests Continuous collision detection (CCD) – 15 elementary tests Culling efficiency

3. Contributions Approach applies to both CD and CCD Feature-based hierarchies – Leaf nodes of (BVH) are features Representative-Triangles (R-Triangles) BVH of AABBs Cloth simulation and N-body collisions

4. Related Work Bounding Volume Hierarchies (BVH) – Recomputed for each frame for deformable models Feature-Based Collision Detection – Largely limited to rigid models Continuous Collision Detection

5. Terminology Feature – vertex, edge, face Contact – collision between feature pairs – Vertex-face (VF) and edge-edge (EE) for CCD – Edge-face for CD Culling Efficiency – number of false positive elementary tests Duplicate Elementary Tests

6. Feature-Based Hierarchies Uses set of independent BVHs – one BVH for each feature type Improves Culling Efficiency – Culling normally on triangles instead of features Each feature represented only once in corresponding hierarchy

7. Representative-Triangles Benefits of feature based hierarches, cost of single hierarchy Contains basic structural data plus – Feature assignments – Feature bounding volumes Every feature is assigned to exactly ONE incident triangle

8. Improved Culling Efficiency R-Triangles replicate functionality of a feature- based hierarchy Only test if triangles represent compatible feature pairs – EE or VF BVs are linked to their R-Triangles eliminates duplicate BV-overlap tests

9. Eliminating Duplicate Queries For each compatible feature pair, the corresponding test is dispatched once Proof based on 3 properties: – I: Every vertex and edge must be represented by a triangle (triangles represent their own faces) – II: Every vertex and edge can be assigned to no more than one triangle – III: If a feature is assigned to a triangle, then it must be incident to that triangle

10. Optimal Representation Assignment schema – which features are assigned to which triangles Maximal schema – feature assignments result in largest number of unassigned triangles Uniform schema – each triangle has the same number of assigned features Optimal assignment schema is possible locally but not globally

12. Implementation Assign features to triangles via a greedy algorithm Representation encoded in 4 bits – Upper 2 for vertices, lower 2 for edges Processing Candidate Triangle Pairs Element BV Type – AABBs Memory Requirements

13. Results Benchmarks – N-body balls, Cloth Ball, Princess, Flamenco Compared against 3 other algorithms for query time and number of elementary tests

14. Analysis/Limitations Duplicate queries eliminated without excessive cost Along with culling, provides increase in performance False positive percentage still over 90%

15. Future Work Integration into Simulation Element Bounding Volumes – Use OBBs or kDOPs instead of AABBs Dynamic Representative Reassignment